Question

What is the strongest classification of the figure formed by the following points?

(–10,-4), (-7,-8), (-5,-4), (-2,-8)
OA. Paralellogram
OB. Quadrilateral
OC. Rectangle
OD. Rhombus

Answer 1

A. Parallelogram

Explanation:

The given points are;

(-10, -4), (-7, -8), (-5, -4), (-2, -8)

Let 'A' represent the point (-10, -4), let 'B' represent the point (-7, -8), let 'C' represent the point (-5, -4), and let 'D' represent the point (-2, -8), we have;

The (horizontal) distance between points A and C = -5 - (-10) = 5

The (horizontal) distance between points B and D = -2 - (-7) = 5

Therefore;

The length of
`\overline {AC}` = The length of
`\overline {BD}`

The length of
`\overline {AB}` = √((-10 - (-7))² + (-4 - (-8))²)) = 5

The length of
`\overline {CD}` = √((-5 - (-2))² + (-4 - (-8))²)) = 5

∴ The length of
`\overline {AB}` = The length of
`\overline {CD}`

`\overline {AC}` is parallel to the horizontal axis

`\overline {BD}` is parallel to the horizontal axis

∴
`\overline {AC}` ║
`\overline {BD}`

Given that
`\overline {AB}` =
`\overline {CD}`, then
`\overline {AB}` ║
`\overline {CD}`

Therefore, the quadrilateral ABCD is a parallelogram

(The angle ∠ABD = 180 - arctan (4/3) ≈ 126.9 > 90, therefore, the parallelogram ABCD is not a rectangle.)